Suppose you group all the stocks in the world into mutually exclusive portfolios $($each stock is in only one portfolio$)$: growth stocks and value stocks. Suppose the two portfolios have equal size $($in terms of total value$),$ a correlation of $0\mathrm{.}5,$ and the following characteristics: Expected Return Value Stock Growth Stocks The risk free$-$rate is $2\%.14\%19\%$ Volatility $11\%23\%$ a$.$ What is the expected return and volatility of the market portfolio $($which is a $50-50$ combination of the two portfolios$)?$ b$.$ Calculate the Sharpe ratios of the value stock, growth stock, and market portfolio. c$.$ Does the CAPM hold in this economy? Explain $($Hint : Is the market portfolio efficient?$)$